Question

excess pressure inside a air bubble

Answer 1

The fact that air has to be blown into a drop of soap solution to make a bubble should suggest that the pressure within the bubble is greater than that outside. This is in fact the case: this excess pressure creates a force that is just balanced by the inward pull of the soap film of the bubble due to its surface tension.

Consider a soap bubble of radius r as shown in Figure 1. Let the external pressure be Po and the internal pressure P1.
The excess pressure P within the bubble is therefore given by :

Excess pressure = P1 - P1

Consider the left-hand half of the bubble. The force acting from right to left due to the internal excess pressure can be shown to be PA, where A is the area of a section through the centre of the bubble. If the bubble is in equilibrium this force is balanced by a force due to surface tension acting from left to right. This force is 2x2πrT (the factor of 2 is necessary because the soap film has two sides) where T is the coefficient of surface tension of the soap film. Therefore

2x2πrT = PA = Pπr2 giving:
Excess pressure in a soap bubble (P) = 4T/r

A bubble of air within a liquid has only one liquid-air surface and the excess pressure within such a bubble is simply:

Excess pressure in an air bubble (P) = 2T/r

Both these formulae show that the excess pressure within a small bubble is greater than that within a larger bubble.

Answer 2

Empty bottles is also contain air when we press the empty bottle in a jar of water the bubbles will come in the water this shows the empty bottle is also having space